Structures algébriques n-aires généralisant les catégories. (n- ary algebraic structures generalizing categories)
type: Item
instance of: scholarly article
title: Structures algébriques n-aires généralisant les catégories. (n- ary algebraic structures generalizing categories)
zbMATH Open document ID: 0687.18001
DOI: 10.1007/BF01229967
author: Vladimir V. Topentcharov
published in: Algebra Universalis
publication date: 1988-01-01T00:00:00Z
review text: In the first chapter the author gives a general algebraic definition of (normal) categories as special partial algebras and four different generalizations of n-categories, where in the case of \(n=2\) these become normal categories. These definitions are ``double categories'', which are generalized to E-n-categories, V-categories, T-n-categories and H-n- categories. In the second chapter the author gives some general results on the considered categories and the forgetful functor \(C\to SET\). The third chapter contains embeddings of the categories in some categories of mappings. Can any n-category in some sense be imbedded in a category derived on a 2-category - like any n-group can be imbedded in a n-group derived by a 2-group (cf. Post ``coset theorem'', 1940)? This question is treated in the fourth chapter. In the fifth chapter it is shown that any n-category can be represented by a category of n endomorphisms such that n-morphisms are products of n morphisms of the category. Finally four open problems in the theory of n-categories are posed. The paper contains a list of 107 papers on different kinds of n- categories.
Mathematics Subject Classification ID: 18A05
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 08A55
Mathematics Subject Classification ID: 08C05
zbMATH DE Number: 4125643
zbMATH Keywords: generalizations of n-categories
zbMATH Keywords: normal categories
MaRDI profile type: Publication
cites work: Q5586439
cites work: Q4693151
cites work: Q5679011
cites work: Q4097071
cites work: Q3848220
cites work: Introduction to bicategories
cites work: On the algebra of cubes
cites work: Q4146875
cites work: Catégories structurées
cites work: Q5586440
cites work: Structures quasi-quotient
cites work: Q5602144
cites work: Formal category theory: Adjointness for 2-categories
cites work: Q3856910
cites work: Q3866264
cites work: Q3885901
cites work: Q5725023
cites work: Q4088973
cites work: Q5552183
cites work: Polycategories
cites work: Q5590086
cites work: Q5634024
cites work: Q4100655
cites work: Q5609436
cites work: Éléments de la théorie des catégories polyadiques
cites work: Recouvrement des {n}-categories
cites work: Q3957113
cites work: Q5187434
cites work: Q5185054
cites work: Q3665295
cites work: Q3665296
cites work: Q3734626
cites work: Q3747739
full work available at URL: https://doi.org/10.1007/bf01229967
OpenAlex ID: W2911660645
description: scientific article; zbMATH DE number 4125643